Convex MR brain image reconstruction via non‐convex total variation minimization

Liu, Yilin; Du, Heng; Wang, Zexian; Mei, Wenbo

doi:10.1002/ima.22275

Cited by 20 publications

(19 citation statements)

References 24 publications

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“…In Table , PSNR values for all five methods are calculated using different types of MRI brain tumor images. Table clearly states that the best PSNR of the proposed method (APDE) is 71.5725 dBs, which is better than the PSNR values of the existing methods such as minmax concave total variation (MCTV‐39.7445 dBs), support vector machine (proposed classifier) (SVM[PC]‐68.2100 dBs), parallel magnetic resonance imaging (PMRI‐43.8339 dBs), modified pyramidal dual‐tree direction filter (MPDTDF‐31.3500 dBs) . This is for denoising …”

Section: Discussionmentioning

confidence: 92%

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Denoising and segmentation of MR images using fourth order non‐linear adaptive PDE and new convergent clustering

Kollem

Reddy²,

Rao

2018

Int J Imaging Syst Tech

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At present, digital image processing plays a vital role in medical imaging areas and specifically in magnetic resonance imaging (MRI) of brain images such as axial and coronal sections. This article mainly focused on the MRI brain images. The existing methods such as total variation (MC), parallel MRI, modified pyramidal dual‐tree direction filter, adaptive dictionary selection algorithm, classifier methods, and fuzzy clustering techniques are poor in image eminence and precision. Thus, this article presents a novel approach consisting of denoising followed by segmentation. The objective of these proposed methods was visual eminence improvement of medical images to examine tumor extent using an adaptive partial differential equation (APDE)‐based analysis with soft threshold function in denoising. The fourth order, nonlinear APDE was used to denoise the image depending on gradient and Laplacian operators associated with the new adaptive Haar‐type wavelet transform. A second approach was the new convergent K‐means clustering for segmentation. The convergent K‐means procedure diminishes the summation of the squared deviations of structures in a cluster from the center. The significance of these proposed methods was to compute their performances in terms of mean squared error, peak signal‐to‐noise ratio, structure similarity, segmentation accuracy, false hit, missed‐term, and elapsed time. The results were analyzed with the MATLAB software.

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Section: Discussionmentioning

confidence: 92%

“…Liu et al recommended minmax concave total variation (MCTV) and applied it to the reconstruction of the MR brain image. MCTV is a method that is compatible with the alternating direction method of the multiplier algorithm.…”

Section: Introductionmentioning

confidence: 99%

Denoising and segmentation of MR images using fourth order non‐linear adaptive PDE and new convergent clustering

Kollem

Reddy²,

Rao

2018

Int J Imaging Syst Tech

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“…Selesnick proposed the non‐convex regularization model (MCTV‐ L 1 ) of

{TV}_{l_{1}} ((), x)

(Equation ), 29 and Liu et al applied the model to MRI reconstruction 36 . This paper will focus on the non‐convex regularization model (MCTV‐ L 2 ) of

{TV}_{l_{2}} ((), x)

(Equation ).…”

Section: Non‐convex Regularization Of Tv Normmentioning

confidence: 99%

“…Similar to References 29 and 36, Equation () can be efficaciously calculated by the following iterative steps (Equations and ):

t^{k} = bold-italicD x^{k + 1} + \frac{{bold-italicu}^{k}}{ρ} + \frac{b}{ρ} ((), z^{k} - l_{2} ((), {bold-italicz}^{k}, \frac{1}{b})),

z^{k + 1} = l_{2} (();, {bold-italict}^{k}, \frac{1}{ρ}),

where

l_{2} (();, y, λ) = \arg \min_{x} \frac{1}{2} {‖y - x‖}_{2}^{2} + λ {‖bold-italicx‖}_{2} .

…”

Section: Admm Algorithm For Mri Reconstructionmentioning

confidence: 99%

“…Most recent research focus on the anisotropic TV regularizer. For example, based on the work of Selesnick, Liu et al 36 proposed a minimum‐maximum concave TV regularization model for L 1 norm (MCTV‐ L 1 ) and used it for MRI reconstruction. As mentioned in Reference 25, anisotropic TV regularizer that can be converted into L 1 norm can cause the sparsity of the sparse image gradient, which is suitable for piecewise constant images with sparse edges, especially those present a “blocky” structure 37 .…”

Section: Introductionmentioning

confidence: 99%

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Magnetic resonance imaging reconstruction via non‐convex total variation regularization

Shen

Zhang

et al. 2020

Int J Imaging Syst Tech

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Magnetic resonance imaging (MRI) reconstruction model based on total variation (TV) regularization can deal with problems such as incomplete reconstruction, blurred boundary, and residual noise. In this article, a non‐convex isotropic TV regularization reconstruction model is proposed to overcome the drawback. Moreau envelope and minmax‐concave penalty are firstly used to construct the non‐convex regularization of L2 norm, then it is applied into the TV regularization to construct the sparse reconstruction model. The proposed model can extract the edge contour of the target effectively since it can avoid the underestimation of larger nonzero elements in convex regularization. In addition, the global convexity of the cost function can be guaranteed under certain conditions. Then, an efficient algorithm such as alternating direction method of multipliers is proposed to solve the new cost function. Experimental results show that, compared with several typical image reconstruction methods, the proposed model performs better. Both the relative error and the peak signal‐to‐noise ratio are significantly improved, and the reconstructed images also show better visual effects. The competitive experimental results indicate that the proposed approach is not limited to MRI reconstruction, but it is general enough to be used in other fields with natural images.

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Diffusion optical tomography reconstruction based on convex–nonconvex graph total variation regularization

Xie

Liu

et al. 2022

Math Methods in App Sciences

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Graph total variation (GTV) is a powerful regularization tool for diffuse optical tomography (DOT) reconstruction since it combines the powerful representation ability of graph and the edge-preserving ability of total variation (TV) regularization. However, as everyone knows, the classical TV regularization trend underestimates the large edge values. In this paper, we propose a convex-nonconvex graph total variation (CNC-GTV) regularization for DOT reconstruction. In particular, we construct a nonconvex regularization by subtracting the generalized Huber function from the GTV regularization. We show that the global convexity of the objective function can be guaranteed by adjusting the nonconvex control parameters. Moreover, we present an alternating direction multiplier method (ADMM) to solve the proposed DOT reconstruction model. Numerical experiments show that the proposed model outperforms existing models in visual and numerical results.

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Convex MR brain image reconstruction via non‐convex total variation minimization

Cited by 20 publications

References 24 publications

Denoising and segmentation of MR images using fourth order non‐linear adaptive PDE and new convergent clustering

Denoising and segmentation of MR images using fourth order non‐linear adaptive PDE and new convergent clustering

Magnetic resonance imaging reconstruction via non‐convex total variation regularization

Diffusion optical tomography reconstruction based on convex–nonconvex graph total variation regularization

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